The saga might not be as bizarre as a red room, a severed ear, or a dumpster monster — but it’s close. A back and forth between a president and an art-house auteur sprung up this week, with a strange and misconstrued endorsement ultimately ending in rejection.

On Saturday, the filmmaker David Lynch was interviewed by The Guardian while promoting “Room to Dream,” his idiosyncratic new biography. He mused on his marriages, the return of “Twin Peaks” — and President Trump. “He could go down as one of the greatest presidents in history because he has disrupted the thing so much,” Mr. Lynch said. “No one is able to counter this guy in an intelligent way.”

The article noted that Mr. Lynch voted for Bernie Sanders in the 2016 primaries and the Libertarian candidate Gary Johnson in the general election, and clarified: “While Trump may not be doing a good job himself, Lynch thinks, he is opening up a space where other outsiders might.” Mr. Lynch added: “Our so-called leaders can’t take the country forward, can’t get anything done. Like children, they are. Trump has shown all this.”

The first quote quickly became a headline across the internet, including on the right-leaning site Breitbart. Mr. Trump, never one to ignore praise about him, quickly tweeted out the piece:

Mr. Trump then went a step further, reading parts of the Breitbart article out loud while onstage at a rally in South Carolina on Monday, and several times repeating and embellishing the line about being “one of the greatest presidents in history.” He called Mr. Lynch a “great filmmaker” and then joked: “Of course, there goes his career in Hollywood.”

On Tuesday, however, Mr. Lynch responded on Facebook with an open letter to Mr. Trump and said that his words had been taken out of context. “Unfortunately, if you continue as you have been, you will not have a chance to go down in history as a great president,” he wrote. “This would be very sad it seems for you — and for the country. You are causing suffering and division.”

He added: “It’s not too late to turn the ship around. Point our ship toward a bright future for all. You can unite the country. Your soul will sing. Under great loving leadership, no one loses — everybody wins. It’s something I hope you think about and take to heart. All you need to do is treat all the people as you would like to be treated.”